The algebra A_{\hbar,η}(\hat{g}) and Infinite Hopf family of algebras

Details The algebra A_{\hbar,η}(\hat{g}) and Infinite Hopf family of algebras The algebra A_{\hbar,η}(\hat{g}) and Infinite Hopf family of algebras

1997-03-30

arxiv.org/abs/q-alg/9703046v3

Mathematics

Quantum Algebra

This version has been completely revised. Many corrections are made. In the title we add the word "infinite" to show the diffe

Scientific paper

10.1016/S0393-0440(97)00079-X

New deformed affine algebras A_{\hbar,\eta}(\hat{g}) are defined for any simply-laced classical Lie algebra g, which are generalizations of the algebra A_{\hbar,\eta}(\hat{sl_2}) recently proposed by Khoroshkin, Lebedev and Pakuliak (KLP). Unlike the work of KLP, we associate to the new algebras the structure of an infinite Hopf family of algebras in contrast to the one containing only finite number of algebras introduced by KLP. Bosonic representation for A_{\hbar,\eta}(\hat{g}) at level 1 is obtained, and it is shown that, by repeated application of Drinfeld-like comultiplications, a realization of A_{\hbar,\eta}(\hat{g}) at any positive integer level can be obtained. For the special case of g=sl_{r+1}, (r+1)-dimensional evaluation representation is given. The corresponding intertwining operators are defined and the intertwining relations are also derived explicitly.

Affiliated with

Also associated with

No associations

Rating

The algebra A_{\hbar,η}(\hat{g}) and Infinite Hopf family of algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The algebra A_{\hbar,η}(\hat{g}) and Infinite Hopf family of algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The algebra A_{\hbar,η}(\hat{g}) and Infinite Hopf family of algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-353960